Topological Data Analysis

Afra Zomorodian

Computer Science, Dartmouth College

We often seek to understand the structure of a set of data points. Generally, we assume that the points are sampled from some underlying space in which we are interested. Many disciplines focus on the geometry of this space, analyzing local properties quantitatively. However, the topology of the space often determines the effectiveness of such geometric algorithms. Topological questions have emerged naturally in many areas of computer science, giving rise to the area of computational topology.

In this talk, I discuss persistent homology, an algebraic method for a multi-scale analysis of a set of points. After describing the theory, I will give a recent application that looks at the local structure of natural images, with possible implications for image compression.

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